BRUSSELS (Reuters) - U.S. President Donald Trump's defense secretary on Thursday said he did not see possible military collaboration with Russia now, in a blow to Moscow's hopes to mend ties with Washington after Trump's election.

The remarks are perhaps the strongest indication yet from the Trump administration that prospects for any significant cooperation between the U.S. and Russian militaries against Islamic State in Syria is unlikely anytime soon.

They came despite repeated suggestions by Trump during his election campaign of the possibility of joint action against Islamic State militants.

"We are not in a position right now to collaborate on a military level. But our political leaders will engage and try to find common ground," Jim Mattis told reporters after talks at NATO headquarters in Brussels, also mentioning U.S. concerns about Russian interference in democratic elections.

Just hours before Mattis spoke, Russian President Vladimir Putin said it was in the interests of both nations to restore communications between their intelligence agencies.

"It's absolutely clear that in the area of counter-terrorism all relevant governments and international groups should work together," he told Russia's Federal Security Service (FSB).

U.S. intelligence agencies, however, are among the most powerful voice of caution in Washington on Russia, concluding that Moscow hacked and leaked Democratic Party emails during the presidential campaign as part of efforts to tilt the vote in the Nov. 8 election in Trump's favor.

Monday's resignation of national security adviser Michael Flynn, who was seen in Moscow as a leading advocate of warmer ties with Russia, has underscored for the Kremlin the difficulties of reaching a settlement.

Flynn resigned after disclosures he had discussed U.S. sanctions on Russia with the Russian ambassador to the United States before Trump took office, and that he later misled Vice President Mike Pence about the conversations.

Asked whether he believed that Russia interfered in U.S. presidential elections, Mattis said: "Right now, I would just say there's very little doubt that they have either interfered or they have attempted to interfere in a number of elections in the democracies." He did not explicitly cite the U.S. election.

A Kremlin aide said there had been no progress on a potential meeting between Trump and Putin. "There is no agreement on a meeting nor a clear understanding yet," Interfax news agency quoted Kremlin aide Yuri Ushakov as saying.

BACK-AND-FORTH

Mattis, who has previously accused Russia of trying to break the NATO alliance, told a closed-door session of NATO on Wednesday that it needed to be realistic about the chances of restoring a cooperative relationship with Moscow.

He cited Moscow's 2014 annexation of Crimea from Ukraine, which plunged U.S.-Russia relations to a post-Cold War low. Mattis said NATO needed "negotiate from a position of strength" as he called for stepped up military spending.

That prompted a terse reply from Russia's Defense Minister Sergei Shoigu. "Attempts to build a dialogue with Russia from a position of strength would be futile," he was quoted as saying by TASS news agency.

Mattis shot back: "I have no need to respond to the Russian statement at all. NATO has always stood for military strength and protection of the democracies and the freedoms we intend to pass on to our children."

The back-and-forth came even as U.S. Secretary of State Rex Tillerson and Russian Foreign Minister Sergei Lavrov met in Germany, and U.S. Marine General Joseph Dunford, the top U.S. military officer, met Chief of the Russian General Staff Valery Gerasimov in Azerbaijan.

Lavrov dismissed the uproar over the U.S. election. "You should know we do not interfere in the domestic matters of other countries," he said.

Congressional inquiries into alleged Russian interference in the U.S. elections are gaining momentum as Capitol Hill investigators press intelligence and law enforcement agencies for access to classified documents.

The FBI and several U.S. intelligence agencies are investigating Russian espionage operations in the United States.

They are also looking at contacts in Russia between Russian intelligence officers or others with ties to Putin's government and people connected to Trump or his campaign.